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April 13th, 2017, 09:53 AM   #1
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How to calculate variance With probability states?

Ok, i came across a problem that stumped me,
I want to preface this question by saying I want to figure-out how to solve it on the TI-84 without manually grinding through the entire equation.

I need to determine the variance of a set of numbers while taking into account the probability of it to begin with, in this example it is setup to look like a return on stock investment.

Probability of economy
Boom .14
Stable .15
Stagnant .52
recession .19

stock yield in boom .3
stock yield in stable .12
stock yield in stagnation .7
stock yield in recession -.15

solve for variance.
I would like to point out I tried just to make a stat list of the yields of the stock and use the variance command on those, and it came up incorrect. I also tried making a second stat list of the probability states and running it through the calculators 2 var statistics program, but its been so many years since i had a statistics class I honestly don't remember what Im looking for, if the result would even be in there.

I found a fairly long and drawn out equation to calculate it by hand, but I've generally learned that their almost always exists an easier way to do it on a TI-84
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April 13th, 2017, 10:05 AM   #2
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variance is just

$E[(x - E[x])^2]=E[x^2]-(E[x])^2$

$E[x] = \displaystyle \sum_k ~p_k x_k$

$E[x^2] = \displaystyle \sum_k ~p_k x_k^2$

Using your numbers, for yield $x$

$E[x] = (0.14)(0.3)+(0.15)(0.12) + (0.52)(0.7) -(0.19)(0.15)=0.3955$

$E[x^2] = (0.14)(0.3)^2+(0.15)(0.12)^2 + (0.52)(0.7)^2 -(0.19)(0.15)^2=0.265285$

$var = E[x^2]-(E[x])^2 = 0.265285 - (0.3955)^2 = 0.108865$
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April 13th, 2017, 12:12 PM   #3
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Thanks for the reply, but I am still struggling to manually work this out, is their a shortcut on the calculator?
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